Indentation-based approach has been implemented to measure material properties of soft materials at nano-scale, including polymers, live biomaterials and food product. For example, by measuring the excitation force applied from the probe to the sample surface and the corresponding indentation generated in the sample, the mechanical properties such as the elastic modulus or the complex compliance (for viscoelastic materials) of the sample can be quantified from the contact mechanics model of the probe-sample interaction dynamics (e.g., the Hertzian model or the DMT model). As the force applied and the indentation generated act as the input and the output, respectively, to the probe-sample interaction contact model, the accuracy of the indentation measurement dictates that of the nano-mechanical properties measured. Therefore, accurate indentation measurement is desirable for the accurate characterization of the nanomechanical properties of soft material.
Atomic Force Microscopes (AFM) have been used to measure nano-mechanical properties of soft materials using an indentation measurement. However, conventional indentation measurement has limitations and results in large errors when the measurement frequency becomes large, or the indentation is measured in liquid. In the method currently used in commercial AFM systems, indentation is obtained from the difference of the AFM cantilever deflection on the specimen and that on a reference hard sample when the same input is applied to drive the z-piezo actuator of the AFM in both measurements. Such a method may be adequate for indentation measurement when the measurement is in air and the measurement frequency is relatively low. However, when the measurement frequency increases and becomes close to the bandwidth of the AFM z-axis dynamics, the instrument hardware dynamics (e.g, the AFM z-dynamics) can be convoluted with the viscoelastic response of the soft specimen, and affect the measured cantilever displacement (i.e., the cantilever deflection). As a result, the indentation obtained is distorted by the instrument hardware dynamics response.
Furthermore, for nano-mechanical measurement in liquid, the motion of the cantilever, unlike that in air, is significantly affected by the thermal drift effect and the hydrodynamic force. Accurate broadband and accurate in-liquid indentation measurements are desired because the mechanical behavior of soft materials is rate-dependent, and materials such as live biological samples (e.g., live cell) are studied in liquid to maintain the behavior and/or chemical and physical properties of these materials. Therefore, there is a need to develop a new approach to nano-indentation measurement of soft materials using AFM.
It is challenging to achieve accurate broadband or in-liquid indentation measurements. Due to the hardware dynamics-viscoelasticity convolution effect during the broadband nano-mechanical measurement, the amplitude of the excitation force applied can be severely distorted and become excessively large at some frequencies and/or excessively small at others, i.e., the measurement suffers from saturation and/or poor signal-to-noise ratio issues. Such a convolution-caused force distortion can be compensated for by using control techniques to track the excitation force on the soft specimen accurately. However, when the same input is applied to a hard sample (for measuring the indentation), dynamics convolution effect on the force-distance measurement of the hard reference sample still exists. This dynamics convolution effect on the indentation measurement is caused by the difference between the nano-mechanical properties of the soft specimen and that of the hard sample, and the difference becomes more pronounced as the measurement frequency range increases (i.e., broadband). Moreover, when measuring the indentation in liquid, the thermal drift effect generates an asymmetric disturbance force on the cantilever (due to the asymmetric geometric configuration of the cantilever), resulting in the fluctuation of the cantilever deflection of random-motion characteristics.
Although feedback control can be used to compensate for the drift effect, the conventional indentation method is generally not compatible with feedback control framework, i.e., under the feedback controller, the input to drive the piezoactuator during the force-distance measurement of the soft sample and that of the hard sample are different, and the same cantilever deflection is obtained on both the soft and the hard samples. Furthermore, errors in the conventional method in-liquid indentation measurement are also caused by the difference of the hydrodynamic force exerting on the cantilever for the soft specimen and that for the hard sample, as the hydrodynamics force depends on the cantilever deflection amplitude and the force load frequency. Moreover, these fundamental limits of the existing conventional indentation measurement cannot be readily addressed through hardware improvement.